🔧 What the Method Does

Introduces a method for scaling two datasets from different sources by estimating a latent factor common to both and idiosyncratic factors unique to each source. The approach also lets the scaled locations depend on covariates and enables efficient inference via resampling.

📐 How the Model Handles Data and Inference

• Models a shared latent factor that captures the subspace common to both datasets.
• Simultaneously estimates idiosyncratic latent factors for each dataset to capture source-specific variation.
• Permits scaled locations to be modeled as functions of covariates to increase flexibility and interpretability.
• Uses an efficient implementation that supports inference through resampling techniques.

🧪 Evidence from Simulations

A simulation study demonstrates that the proposed method outperforms existing alternatives in two respects:

• Better recovery of the variation common to both datasets.
• Improved identification of latent factors that are specific to each dataset.

🏛️ Applied Example: Votes and Speeches in the 112th U.S. Senate

• Applied the method to roll-call voting and speech data from the 112th U.S. Senate.
• Recovered a shared subspace that aligns with a standard ideological dimension running from liberals to conservatives.
• Identified the words most strongly associated with each senator's position in that shared subspace.
• Estimated a word-specific subspace that spans topics from national security to budget concerns.
• Estimated a vote-specific subspace that places Tea Party senators at one extreme and senior committee leaders at the other.

⚖️ Why It Matters

Provides a practical and flexible way to combine different data sources (e.g., text and votes) to uncover both shared political dimensions and source-specific signals, with usable inference for applied political science work.